Question

$15-20=$ Minors and Cofactors Evaluate the minor and cofactor using the matrix $A .$ $$A=\left[ \begin{array}{rrr}{1} & {0} & {\frac{1}{2}} \\ {-3} & {5} & {2} \\ {0} & {0} & {4}\end{array}\right]$$ $$ M_{33}, A_{33} $$

Name: Problem 16, Chapter 11: Algebra and Trigonometry
Uploaded: 2019-06-28T04:43:16-08:00
Duration: 1 min 51 s
Channel: Kaitlyn Wu
Description: 15-20= Minors and Cofactors Evaluate the minor and cofactor using the matrix A . A=[ 1 0 (1)/(2) -3 5 2 0 0 4 ] M33, A33

   $15-20=$ Minors and Cofactors Evaluate the minor and cofactor
using the matrix $A .$

$$A=\left[ \begin{array}{rrr}{1} & {0} & {\frac{1}{2}} \\ {-3} & {5} & {2} \\ {0} & {0} & {4}\end{array}\right]$$

$$
M_{33}, A_{33}
$$

Algebra and Trigonometry

James Stewart,… 4th Edition

Chapter 11, Problem 16

Instant Answer

Solved by Expert Kaitlyn Wu

06/28/2019

Step 1

To do this, we delete the third row and the third column of the matrix $A$. This leaves us with the following 2x2 matrix: $$ \left[ \begin{array}{rr}{1} & {0} \\ {-3} & {5} \end{array}\right] $$ Show more…

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$15-20=$ Minors and Cofactors Evaluate the minor and cofactor using the matrix $A .$ $$A=\left[ \begin{array}{rrr}{1} & {0} & {\frac{1}{2}} \\ {-3} & {5} & {2} \\ {0} & {0} & {4}\end{array}\right]$$ $$ M_{33}, A_{33} $$

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Key Concepts

Matrix

A matrix is a rectangular array of numbers or symbols arranged in rows and columns, used to represent and solve systems of linear equations, perform linear transformations, and organize data for various computations in linear algebra.

Minor

A minor of an element in a matrix is defined as the determinant of the submatrix that remains after removing the row and column of that particular element. It plays a significant role in the processes of finding determinants and in formulating cofactors.

Cofactor

A cofactor is closely related to a minor and is calculated by multiplying the minor by (-1) raised to the sum of the row and column indices (i+j) of the element. Cofactors are essential for performing cofactor expansion, a method used to compute the determinant of a matrix.

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